Safford is a city in Graham County, Arizona, United States. According to the 2020 Census, the population of the city is 10,129. The city is the …Safford is a city in Graham County, Arizona, United States. According to the 2020 Census, the population of the city is 10,129. The city is the county seat of Graham County. Safford is the principal city of the Safford Micropolitan Statistical Area, which includes all of Graham County.